matlab求矩阵的特征值与特征向量介绍.doc

使用matlab求矩阵的特征值和特征向量介绍v,d=eig(A);A为你的矩阵，V为特征向量矩阵，D为特征值矩阵，然后对D求最大值即可得最大特征根！V,D = EIG(X) produces a diagonal matrix D of eigenvalues and a full matrix V whose columns are the corresponding eigenvectors so that X*V = V*D.V是特征向量，D是特征值实例：矩阵：1 2/3 7/3 7/33/2 1 3/2 3/23/7 2/3 1 3/23/7 2/3 2/3 1 format rat A=1 2/3 7/3 7/33/2 1 3/2 3/23/7 2/3 1 3/23/7 2/3 2/3 1A =1 2/3 7/3 7/33/2 1 3/2 3/23/7 2/3 1 3/23/7 2/3 2/3 1 V,D=eig(A)V =1793/2855 504/3235 - 146/235i 504/3235 + 146/235i 1990/4773670/1079 -3527/5220 -3527/5220 -509/9594350/11989 1160/4499 + 287/3868i 1160/4499 - 287/3868i -350/647838/2819 181/3874 + 1179/4852i 181/3874 - 1179/4852i 1238/2467D =810/197 0 0 00 -93/4229 + 455/674i 0 00 0 -93/4229 - 455/674i 00 0 0 -149/2201如何归一化求权重呢？ a=1 3 5;1/3 1 3; 1/5 1/3 1a =1.00003.00005.00000.33331.00003.00000.20000.33331.0000 V,D=eig(a)V =0.91610.91610.91610.3715-0.1857 + 0.3217i-0.1857 - 0.3217i0.1506-0.0753 - 0.1304i-0.0753 + 0.1304iD =3.0385000-0.0193 + 0.3415i000-0.0193 - 0.3415i* a=1 2 4 8 6 6 8;1/2 1 2 6 4 4 8;1/4 1/2 1 4 2 4 6;1/8 1/6 1/4 1 2 2 4;1/6 1/4 1/2 1/2 1 1 4;1/6 1/4 1/4 1/2 1 1 2;1/8 1/8 1/6 1/4 1/4 1/2 1a =1.00002.00004.00008.00006.00006.00008.00000.50001.00002.00006.00004.00004.00008.00000.25000.50001.00004.00002.00004.00006.00000.12500.16670.25001.00002.00002.00004.00000.16670.25000.50000.50001.00001.00004.00000.16670.25000.25000.50001.00001.00002.00000.12500.12500.16670.25000.25000.50001.0000 rats(a)ans =12486681/21264481/41/2142461/81/61/412241/61/41/21/21141/61/41/41/21121/81/81/61/41/41/21 V,D=eig(a)V =0.78840.83270.83270.80830.8083-0.5119 + 0.3865i-0.5119 - 0.3865i0.48940.3216 + 0.2636i0.3216 - 0.2636i0.1760 + 0.0792i0.1760 - 0.0792i0.67830.67830.30380.0883 + 0.2728i0.0883 - 0.2728i-0.4630 + 0.1038i-0.4630 - 0.1038i-0.2011 - 0.2400i-0.2011 + 0.2400i0.1404-0.1620 + 0.1018i-0.1620 - 0.1018i0.0620 - 0.0510i0.0620 + 0.0510i-0.0006 + 0.1021i-0.0006 - 0.1021i0.1215-0.0627 - 0.0658i-0.0627 + 0.0658i0.0367 + 0.2360i0.0367 - 0.2360i-0.0531 + 0.0357i-0.0531 - 0.0357i0.0975-0.0303 - 0.0476i-0.0303 + 0.0476i0.0488 - 0.1148i0.0488 + 0.1148i0.0231 - 0.1221i0.0231 + 0.1221i0.05080.0030 - 0.0590i0.0030 + 0.0590i-0.0561 - 0.0454i-0.0561 + 0.0454i0.0102 + 0.0197i0.0102 - 0.0197iD =7.38990000000-0.0008 + 1.5369i00